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Design and Gait Analysis of a Two-legged Miniature Robot with Piezoelectric-driven Four-bar Linkage

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This paper presents the design and development of a new
type of piezoelectric-driven robot, which consists of a piezoelectric
unimorph actuator integrated as part of the structure of a
four-bar linkage to generate locomotion. The unimorph actuator
replaces the input link of the four-bar linkage and motion is generated
at the coupler link due to the actuator deflection. A dimensional
synthesis approach is proposed for the design of four-bar
linkage that amplifies the small displacement of the piezoelectric
actuator at the coupler link. The robot consists of two such
piezo-driven four-bar linkages and its gait cycle is described. The
robot speed is derived through kinematic modelling and experimentally
verified using a fabricated prototype. This result will be
important for developing a motion planning control strategy for
the robot locomotion, which will be part of future work.

Published in: Engineering
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Design and Gait Analysis of a Two-legged Miniature Robot with Piezoelectric-driven Four-bar Linkage

  1. 1. 1 Prof. Kevin Otto, Prof. Soh Gim Song, Prof. Foong Shaohui, Hanson Chen Xiaohan, Blake William Clark Sedore, Audelia Gumarus DharmawanDesign and Gait Analysis of a Two-legged Miniature Robot with Piezoelectric-driven Four-bar Linkage Audelia G. Dharmawan, Hassan H. Hariri, Gim Song Soh, Shaohui Foong, and Kristin L. Wood
  2. 2. 2 Prof. Kevin Otto, Prof. Soh Gim Song, Prof. Foong Shaohui, Hanson Chen Xiaohan, Blake William Clark Sedore, Audelia Gumarus Dharmawan Introduction Miniature mobile robots Light weight, small size Swarming and distributed sensing Tight spaces inaccessible by human Dharmawan et al., 2017 Son et al., 2006 Ho et al., 2009 Rios et al., 2017 Baisch, 2013 Avirovik et al., 2014 Piezoelectric Actuator Image from http://www.militaryaerospace.com Image from http://www.militaryaerospace.com Image from http://blog.ascens-ist.eu
  3. 3. 3 Prof. Kevin Otto, Prof. Soh Gim Song, Prof. Foong Shaohui, Hanson Chen Xiaohan, Blake William Clark Sedore, Audelia Gumarus Dharmawan Problem Limited displacement of piezoelectric actuator Amplification through linkage mechanism to achieve larger stroke Some linkage mechanism Adapted from Sahai, 2006
  4. 4. 4 Prof. Kevin Otto, Prof. Soh Gim Song, Prof. Foong Shaohui, Hanson Chen Xiaohan, Blake William Clark Sedore, Audelia Gumarus Dharmawan Literature Review Common approach of choosing the geometric parameters of the linkages: • Arbitrarily • Optimization No technique exists for a task-oriented design of piezo-driven mechanism that achieves a required stroke amplification or gait trajectory Multiple four bar Five bar Spherical five bar Sitti, 2003 Goldfarb et al., 2001 Baisch et al., 2010
  5. 5. 5 Prof. Kevin Otto, Prof. Soh Gim Song, Prof. Foong Shaohui, Hanson Chen Xiaohan, Blake William Clark Sedore, Audelia Gumarus Dharmawan Objective • Formulate a design methodology for selecting parameters for the design of piezo-driven legged robots through the use of 4-bar linkages.
  6. 6. 6 Prof. Kevin Otto, Prof. Soh Gim Song, Prof. Foong Shaohui, Hanson Chen Xiaohan, Blake William Clark Sedore, Audelia Gumarus Dharmawan Outline Dimensional Synthesis • Joint limit identification • Design for stroke amplification Gait Analysis • Gait cycle modeling • Mathematical modeling of robot motion Experimental Verification • Robot prototype • Experimental Results Dimensional Synthesis Gait Analysis Experimental Verification
  7. 7. 7 Prof. Kevin Otto, Prof. Soh Gim Song, Prof. Foong Shaohui, Hanson Chen Xiaohan, Blake William Clark Sedore, Audelia Gumarus Dharmawan Unimorph Actuator Dimensional Synthesis Gait Analysis Experimental Verification
  8. 8. 8 Prof. Kevin Otto, Prof. Soh Gim Song, Prof. Foong Shaohui, Hanson Chen Xiaohan, Blake William Clark Sedore, Audelia Gumarus Dharmawan Dimensional Synthesis Restriction: • Actuator length • Actuator displacement Requirement: • Amplification factor Dimensional Synthesis Gait Analysis Experimental Verification
  9. 9. 9 Prof. Kevin Otto, Prof. Soh Gim Song, Prof. Foong Shaohui, Hanson Chen Xiaohan, Blake William Clark Sedore, Audelia Gumarus Dharmawan Joint Limit Identification • Equation of motion (Hariri et al., 2011): (𝐸𝐼) 𝑒𝑞 𝜕2 𝑤(𝑥) 𝜕𝑥2 = −𝑞𝑒 𝑝 𝐸𝑧 • With fixed-free boundary conditions, displacement: 𝑤 𝑥 = −𝑞𝑒 𝑝 𝐸𝑧 2(𝐸𝐼) 𝑒𝑞 𝑥2 • Angular displacement: ζ ≈ 𝑤(𝑙) 𝑙 • Joint limits: 𝜃1,𝑚𝑖𝑛 = 𝜃1,0 − ζ 𝜃1,𝑚𝑎𝑥 = 𝜃1,0 + ζ Dimensional Synthesis Gait Analysis Experimental Verification 𝜃1,𝑚𝑖𝑛 𝜃1,𝑚𝑎𝑥
  10. 10. 10 Prof. Kevin Otto, Prof. Soh Gim Song, Prof. Foong Shaohui, Hanson Chen Xiaohan, Blake William Clark Sedore, Audelia Gumarus Dharmawan Design for Amplification • Introduce a stroke amplification (𝛼): 𝜃2,𝑚𝑖𝑛 = 𝜃2,0 − 𝛼ζ 𝜃2,𝑚𝑎𝑥 = 𝜃2,0 + 𝛼ζ • Choose five task positions from this range for the synthesis of four-bar linkage: 𝑇 = 𝐺 𝑍(𝜃1) 𝑋(𝑎) 𝑍(𝜃2) [𝐻] Dimensional Synthesis Gait Analysis Experimental Verification 𝜃1,𝑚𝑖𝑛 𝜃1,𝑚𝑎𝑥 𝜃2,𝑚𝑖𝑛 𝜃2,𝑚𝑎𝑥
  11. 11. 11 Prof. Kevin Otto, Prof. Soh Gim Song, Prof. Foong Shaohui, Hanson Chen Xiaohan, Blake William Clark Sedore, Audelia Gumarus Dharmawan Outline Dimensional Synthesis • Joint limit identification • Design for stroke amplification Gait Analysis • Gait cycle modeling • Mathematical modeling of robot motion Experimental Verification • Robot prototype • Experimental Results Dimensional Synthesis Gait Analysis Experimental Verification
  12. 12. 12 Prof. Kevin Otto, Prof. Soh Gim Song, Prof. Foong Shaohui, Hanson Chen Xiaohan, Blake William Clark Sedore, Audelia Gumarus Dharmawan Gait Cycle Model Dimensional Synthesis Gait Analysis Experimental Verification High Speed Camera @ 12.5 KHz
  13. 13. 13 Prof. Kevin Otto, Prof. Soh Gim Song, Prof. Foong Shaohui, Hanson Chen Xiaohan, Blake William Clark Sedore, Audelia Gumarus Dharmawan Gait Cycle Model Front Leg Stance Back Leg Stance Dimensional Synthesis Gait Analysis Experimental Verification
  14. 14. 14 Prof. Kevin Otto, Prof. Soh Gim Song, Prof. Foong Shaohui, Hanson Chen Xiaohan, Blake William Clark Sedore, Audelia Gumarus Dharmawan Mathematical Modeling 𝑊 𝑶 𝜃 = − 𝑉 𝑳 𝜃 = −𝐿 𝑥(𝜃) −𝐿 𝑦(𝜃) 𝑊 𝑳′ 𝜃 = 𝑊 𝑶 𝜃 + 𝑉 𝑳′ Dimensional Synthesis Gait Analysis Experimental Verification 𝑉 𝑳 𝜃 = 𝐿 𝑥(𝜃) 𝐿 𝑦(𝜃)
  15. 15. 15 Prof. Kevin Otto, Prof. Soh Gim Song, Prof. Foong Shaohui, Hanson Chen Xiaohan, Blake William Clark Sedore, Audelia Gumarus Dharmawan Mathematical Modeling 𝑶 𝑎 = 𝑊 𝑶(𝜃 𝑚𝑖𝑛) 𝑶 𝑏 = 𝑊 𝑶(𝜃0) 𝑶 𝑐 = 𝑊 𝑶(𝜃 𝑚𝑎𝑥) 𝑳′ 𝑐 = 𝑊 𝑳′ 𝜃 𝑚𝑎𝑥 𝑶 𝑑 = 𝑍(𝛾′ ) 𝑶 𝑐 𝑺 𝑎𝑑 = 𝑶 𝑑 − 𝑶 𝑎 Dimensional Synthesis Gait Analysis Experimental Verification W W W W
  16. 16. 16 Prof. Kevin Otto, Prof. Soh Gim Song, Prof. Foong Shaohui, Hanson Chen Xiaohan, Blake William Clark Sedore, Audelia Gumarus Dharmawan Mathematical Modeling 𝑊′ 𝑶 𝑑 = 𝑊′ 𝑳 + 𝑶 𝑑 𝑶 𝑓 = 𝑶 𝑒 = 𝑊′ 𝑶 𝑑 𝑶 𝑔 = 𝑍(𝛾) 𝑶 𝑓 𝑺 𝑑𝑔 = 𝑶 𝑔 − 𝑊′ 𝑶 𝑑 𝑺 𝑔𝑎𝑖𝑡 = 𝑺 𝑎𝑑 + 𝑺 𝑑𝑔 Dimensional Synthesis Gait Analysis Experimental Verification W’ W’ W’ W’ 𝑉𝑏𝑜𝑡 = 𝑓 ∗ 𝑆 𝑔𝑎𝑖𝑡,𝑥 ≈ 𝑓 ∗ 𝐿 𝑥 𝜃 𝑚𝑖𝑛 − 𝐿 𝑥(𝜃 𝑚𝑎𝑥)
  17. 17. 17 Prof. Kevin Otto, Prof. Soh Gim Song, Prof. Foong Shaohui, Hanson Chen Xiaohan, Blake William Clark Sedore, Audelia Gumarus Dharmawan Outline Dimensional Synthesis • Joint limit identification • Design for stroke amplification Gait Analysis • Gait cycle modeling • Mathematical modeling of robot motion Experimental Verification • Robot prototype • Experimental Results Dimensional Synthesis Gait Analysis Experimental Verification
  18. 18. 18 Prof. Kevin Otto, Prof. Soh Gim Song, Prof. Foong Shaohui, Hanson Chen Xiaohan, Blake William Clark Sedore, Audelia Gumarus Dharmawan Robot Prototype Dimensional Synthesis Results Properties of the Unimorph Actuator • Dimension: 100 x 17.4 x 27.2 mm • Mass = 12.17 g Dimensional Synthesis Gait Analysis Experimental Verification
  19. 19. 19 Prof. Kevin Otto, Prof. Soh Gim Song, Prof. Foong Shaohui, Hanson Chen Xiaohan, Blake William Clark Sedore, Audelia Gumarus Dharmawan Experimental Results Dimensional Synthesis Gait Analysis Experimental Verification
  20. 20. 20 Prof. Kevin Otto, Prof. Soh Gim Song, Prof. Foong Shaohui, Hanson Chen Xiaohan, Blake William Clark Sedore, Audelia Gumarus Dharmawan Conclusion • Propose a design methodology for selecting parameters for the design of piezo-driven robots • Perform gait and kinematic analysis to predict the motion of the robot • Fabricate a prototype of the robot and conduct experimental test Dimensional Synthesis • Joint limit identification • Design for stroke amplification Gait Analysis • Gait cycle modeling • Mathematical modeling of robot motion Experimental Verification • Robot prototype • Experimental Results
  21. 21. 21 Prof. Kevin Otto, Prof. Soh Gim Song, Prof. Foong Shaohui, Hanson Chen Xiaohan, Blake William Clark Sedore, Audelia Gumarus Dharmawan Future Work Smolka et al., 2013

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